# Analysis of a post-fracture - Constant-rate flow test with boundary effects

## Input(s)

$$\mathrm{q}_{\mathrm{g}}$$: Gas Flow Rate (MSCF/day)

$$\mathrm{B}_{\mathrm{g}}$$: Gas formation Volume Factor $$(\mathrm{RB} / \mathrm{MSCF})$$

$$\mathrm{m}$$: Slope from Curve (psi/cycle)

$$\mathrm{m}_{\mathrm{L}}$$: Slope from linear Region of Curve (psi/cycle)

$$\mathrm{p}_{\mathrm{ai}}$$: Initial Adjusted Well Pressure (psi)

$$\mathrm{p}_{\mathrm{ahr}}$$: Adjusted Well pressure at $$t=1 \mathrm{~h}(\mathrm{psi})$$

$$\mathrm{p}_{\mathrm{D}}$$: Dimensionless Pressure (dimensionless)

Ø: Porosity (dimensionless)

$$\mathrm{c}_{\mathrm{t}}$$: Compressibility (1/psi)

$$\mathrm{r}_{\mathrm{w}}$$: Radius of Wellbore $$(\mathrm{ft})$$

$$\mu$$: Viscosity $$(\mathrm{cP})$$

$$\mathrm{h}$$: Formation Thickness ( $$\mathrm{ft}$$ )

$$t_{L f D}$$: Time of end of Linear or Pseudo Radial flow from Plot (dimensionless)

$$\Delta \mathrm{t}_{\mathrm{a}}$$: Adjusted Delta Time from Derivative Curve (h)

## Output(s)

$$\mathrm{k}$$: Permeability $$(\mathrm{mD})$$

$$\mathrm{L}_{\mathrm{fPR}}$$: Length of Fracture for Pseudo Radial Flow (ft)

$$\mathrm{L}_{\mathrm{fL}}$$: Length of Fracture for Linear Flow (ft)

$$\mathrm{L}_{\mathrm{fMP}}$$: Length of Fracture from Match Point Analysis $$(\mathrm{ft})$$

$$\mathrm{s}$$: Skin Factor (dimensionless)

$$\Delta \mathrm{P}_{\mathrm{a}_{\mathrm{MP}}}$$: Adjusted Pressure Difference at Match Point from Plot (psi)

## Formula(s)

$\begin{gathered} \mathrm{k}=162.6 * \mathrm{q}_{\mathrm{g}} * \mathrm{~B}_{\mathrm{g}} * \frac{\mu}{\mathrm{m} * \mathrm{~h}} \\ \mathrm{~L}_{\mathrm{fPR}}=1.151 *\left(\left(\frac{\mathrm{p}_{\mathrm{ai}}-\mathrm{p}_{\mathrm{ahr}}}{\mathrm{m}}\right)-\log \left(\frac{\mathrm{k}}{\emptyset * \mu * \mathrm{c}_{\mathrm{t}} * \mathrm{r}_{\mathrm{w}}^{2}}\right)+3.23\right) \\ \mathrm{L}_{\mathrm{fL}}=2 * \mathrm{r}_{\mathrm{w}} * 2.71^{-\mathrm{s}} \\ \mathrm{L}_{\mathrm{fMP}}=4.064 * \mathrm{q}_{\mathrm{g}} * \frac{\mathrm{B}_{\mathrm{g}}}{\mathrm{m}_{\mathrm{L}} * \mathrm{~h} * \mathrm{k}^{0.5}} *\left(\left(\frac{\mu}{\varnothing} * \mathrm{c}_{\mathrm{t}}\right)^{\frac{1}{2}}\right) \\ \mathrm{s}=\left(141.2 * \mathrm{q}_{\mathrm{g}} * \mathrm{~B}_{\mathrm{g}} * \frac{\mu}{\mathrm{k}} * \mathrm{~h}\right) *\left(\mathrm{p}_{\mathrm{D}}\right) \\ \Delta \mathrm{P}_{\mathrm{a}_{\mathrm{MP}}}=\left(\left(\frac{0.0002637 * \mathrm{k}}{\varnothing * \mu * \mathrm{c}_{\mathrm{t}}}\right) *\left(\frac{\Delta \mathrm{t}_{\mathrm{a}}}{\mathrm{t}_{\mathrm{LfD}}}\right)\right)^{\frac{1}{2}} \end{gathered}$

## Reference(s)

Lee, J., Rollins J.B., and Spivey J.P. 2003, Pressure Transient Testing, Vol. 9, SPE Textbook Series, Vol. 9, Henry L. Doherty Memorial Fund of AIME, Richardson, Texas, SPE, Chapter: 6, Page: 121.

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